Research
statement

I
am interested in number theory and p-adic analysis. My research focuses on studying
the relationships between the pseudo differential equations and the Markov
processes. To this end, I have used a lot of techniques from number theory and
classical theory of differential equations. Some of the equations that I have
studied include the p-adic heat equation and some generalizations of this using
homogeneous polynomials instead of the classical laplacian. Furthermore, I have
applied the theory of the Igusa’s local zeta function for finding a closed form
for the solution of the p-adic heat equation. All these models have attracted people’s
attention since the mid 80’s because of their relation with alternative models
for quantum mechanics. Also, there is a lot of attention from outside of the
mathematics because of the connection with some models in statistical physics.
For example, people know that some proteins have very complex hierarchical
structures and the setting of p-adic analysis is well suited for this. My long
term research agenda is to study a broad class of pseudo differential equations
that have a probabilistic interpretation and to use the tools of the side of
the equation for obtaining new probabilistic models.

Wow! This is a wonderful research statement. It is very clear and coherent. Excellent job!

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